Inspired by the effectiveness of tree kernels, we investigate the problem of integrating such structured notion into deep learning models. Conversely to well-known tree compliant solutions, such as Recursive Neural Networks (RecNN) [1]} and Tree-LSTM [2]}, we formulate the task of learning structured node clusters as the building block features of the input graph. In particular, the problem of extracting kernel specific tree fragments is viewed as a node soft assignment task by constraining the pooling operation. Each pooled node cluster should be compliant to a specific tree definition, dictated by a given tree kernel.
Differently from node clustering, tree extraction does not necessarily impose mutually exclusive assignments. In most cases, node sharing between extracted trees is unavoidable due to the given fragment definition (e.g., for the STK).
